Problem: Given $ m \angle MON = 5x - 11$, and $ m \angle LOM = 8x + 87$, find $m\angle MON$. $O$ $L$ $N$ $M$
Answer: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {8x + 87} + {5x - 11} = {180}$ Combine like terms: $ 13x + 76 = 180$ Subtract $76$ from both sides: $ 13x = 104$ Divide both sides by $13$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 5({8}) - 11$ Simplify: $ {m\angle MON = 40 - 11}$ So ${m\angle MON = 29}$.